5. (8 points) Medical case histories indicate that different illnesses may produce identical symptoms. Sup- pose a particular set of symptoms, which we will denote as event H, occurs only when any one of three illnesses - A, B or C - occurs. (For simplicity, we will assum that illnesses A, B, and C' are mutually exclusive.) Studies show these probabilities of getting the three illnesses: P(A) = .01, P(B) = .005, P(C) = .02. The probabiities of developing the symptoms H, given a specific illness are P(H|A) = .90, P(H B) = .95, P(HIC).75. Assuming that an ill person shows the symptoms H, what is the probability that the person has illness